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Title: The Birth-Time Of The World Author: John Joly [More Titles by Joly] [A lecture delivered before the Royal Dublin Society, February 6th, 1914. _Science Progress_, vol. ix., p. 37]
Thus spake Lucretius nearly 2,000 years ago. Since then we have attained another standpoint and found very different limitations. To Lucretius the world commenced with man, and the answer he would give to his questions was in accord with his philosophy: he would date the birth-time of the world from the time when poets first sang upon the earth. Modern Science has along with the theory that the Earth dated its beginning with the advent of man, swept utterly away this beautiful imagining. We can, indeed, find no beginning of the world. We trace back events and come to barriers which close our vista--barriers which, for all we know, may for ever close it. They stand like the gates of ivory and of horn; portals from which only dreams proceed; and Science cannot as yet say of this or that dream if it proceeds from the gate of horn or from that of ivory. In short, of the Earth's origin we have no certain knowledge; nor can we assign any date to it. Possibly its formation was an event so gradual that the beginning was spread over immense periods. We can only trace the history back to certain events which may with considerable certainty be regarded as ushering in our geological era. Notwithstanding our limitations, the date of the birth-time of our geological era is the most important date in Science. For in taking into our minds the spacious history of the universe, the world's age must play the part of time-unit upon which all our conceptions depend. If we date the geological history of the Earth by thousands of years, as did our forerunners, we must shape our ideas of planetary time accordingly; and the duration of our solar system, and of the heavens, becomes comparable with that of the dynasties of ancient nations. If by millions of years, the sun and stars are proportionately venerable. If by hundreds or thousands of millions of years the human mind must consent to correspondingly vast epochs for the duration of material changes. The geological age plays the same part in our views of the duration of the universe as the Earth's orbital radius does in our views of the immensity of space. Lucretius knew nothing of our time-unit: his unit was the life of a man. So also he knew nothing of our space-unit, and he marvels that so small a body as the sun can shed so much, heat and light upon the Earth. A study of the rocks shows us that the world was not always what it now is and long has been. We live in an epoch of denudation. The rains and frosts disintegrate the hills; and the rivers roll to the sea the finely divided particles into which they have been resolved; as well as the salts which have been leached from them. The sediments collect near the coasts of the continents; the dissolved matter mingles with the general ocean. The geologist has measured and mapped these deposits and traced them back into the past, layer by layer. He finds them ever the same; sandstones, slates, limestones, etc. But one thing is not the same. _Life_ grows ever less diversified in character as the sediments are traced downwards. Mammals and birds, reptiles, amphibians, fishes, die out successively in the past; and barren sediments ultimately succeed, leaving the first beginnings of life undecipherable. Beneath these barren sediments lie rocks collectively differing in character from those above: mainly volcanic or poured out from fissures in the early crust of the Earth. Sediments are scarce among these materials.[1]
It is from this epoch we date our geological age. Our next purpose is to consider how long ago, measured in years, that birth-time was. That the geological age of the Earth is very great appears from what we have already reviewed. The sediments of the past are many miles in collective thickness: yet the feeble silt of the rivers built them all from base to summit. They have been uplifted from the seas and piled into mountains by movements so slow that during all the time man has been upon the Earth but little change would have been visible. The mountains have again been worn down into the ocean by denudation and again younger mountains built out of their redeposited materials. The contemplation of such vast events prepares our minds to accept many scores of millions of years or hundreds of millions of years, if such be yielded by our calculations.
THE AGE AS INFERRED FROM THE THICKNESS OF THE SEDIMENTS The earliest recognised method of arriving at an estimate of the Earth's geological age is based upon the measurement of the collective sediments of geological periods. The method has undergone much revision from time to time. Let us briefly review it on the latest data. The method consists in measuring the depths of all the successive sedimentary deposits where these are best developed. We go all over the explored world, recognising the successive deposits by their fossils and by their stratigraphical relations, measuring their thickness and selecting as part of the data required those beds which we believe to most completely represent each formation. The total of these measurements would tell us the age of the Earth if their tale was indeed complete, and if we knew the average rate at which they have been deposited. We soon, however, find difficulties in arriving at the quantities we require. Thus it is not easy to measure the real thickness of a deposit. It may be folded back upon itself, and so we may measure it twice over. We may exaggerate its thickness by measuring it not quite straight across the bedding or by unwittingly including volcanic materials. On the other hand, there may be deposits which are inaccessible to us; or, again, an entire absence of deposits; either because not laid down in the areas we examine, or, if laid down, again washed into the sea. These sources of error in part neutralise one another. Some make our resulting age too long, others make it out too short. But we do not know if a balance of error does not still remain. Here, however, is a table of deposits which summarises a great deal of our knowledge of the thickness of the stratigraphical accumulations. It is due to Sollas.[1] [1] Address to the Geol. Soc. of London, 1509.
In the next place we require to know the average rate at which these rocks were laid down. This is really the weakest link in the chain. The most diverse results have been arrived at, which space does not permit us to consider. The value required is most difficult to determine, for it is different for the different classes of material, and varies from river to river according to the conditions of discharge to the sea. We may probably take it as between two and six inches in a century. Now the total depth of the sediments as we see is about 335,000 feet (or 64 miles), and if we take the rate of collecting as three inches in a hundred years we get the time for all to collect as 134 millions of years. If the rate be four inches, the time is soo millions of years, which is the figure Geikie favoured, although his result was based on somewhat different data. Sollas most recently finds 80 millions of years.[1]
THE AGE AS INFERRED FROM THE MASS OF THE SEDIMENTS In the above method we obtain our result by the measurement of the linear dimensions of the sediments. These measurements, as we have seen, are difficult to arrive at. We may, however, proceed by measurements of the mass of the sediments, and then the method becomes more definite. The new method is pursued as follows: The total mass of the sediments formed since denudation began may be ascertained with comparative accuracy by a study of the chemical composition of the waters of the ocean. The salts in the ocean are undoubtedly derived from the rocks; increasing age by age as the latter are degraded from their original character under the action of the weather, etc., and converted to the sedimentary form. By comparing the average chemical composition of these two classes of material--the primary or igneous rocks and the sedimentary--it is easy to arrive at a knowledge of how much of this or that constituent was given to the ocean by each ton of primary rock which was denuded to the sedimentary form. This, however, will not assist us to our object unless the ocean has retained the salts shed into it. It has not generally done so. In the case of every substance but one the ocean continually gives up again more or less of the salts supplied to it by the rivers. The one exception is the element sodium. The great solubility of its salts has protected it from abstraction, and it has gone on collecting during geological time, practically in its entirety. This gives us the clue to the denudative history of the Earth. The process is now simple. We estimate by chemical examination of igneous and sedimentary rocks the amount of sodium which has been supplied to the ocean per ton of sediment produced by denudation. We also calculate the amount of sodium contained in the ocean. We divide the one into the other (stated, of course, in the same units of mass), and the quotient gives us the number of tons of sediment. The most recent estimate of the sediments made in this manner affords 56 x 1016 tonnes.[1]
The river supply of detrital sediment has not been very extensively investigated, although the quantities involved may be found with comparative ease and accuracy. The following table embodies the results obtained for some of the leading rivers.[1] [1] Russell, _River Development_ (John Murray, 1888).
We see that the ratio of the weight of water to the weight of transported sediment in six out of the nine rivers does not vary widely. The mean is 2,730 to 1. But this is not the required average. The water-discharge of each river has to be taken into account. If we ascribe to the ratio given for each river the weight proper to the amount of water it discharges, the proportion of weight of water to weight of sediment, for the whole quantity of water involved, comes out as 2,520 to 1. Now if this proportion holds for all the rivers of the world--which collectively discharge about 27 x 1012 tonnes of water per annum--the river-born detritus is 1.07 x 1010 tonnes. To this an addition of 11 per cent. has to be made for silt pushed along the river-bed. On these figures the minor limit to the age comes out as 47 millions of years, and the major limit as 188 millions. We are here going on rather deficient estimates, the rivers involved representing only some 6 per cent. of the total river supply of water to the ocean. But the result is probably not very far out. We may arrive at a probable age lying between the major and minor limits. If, first, we take the arithmetic mean of these limits, we get 117 millions of years. Now this is almost certainly excessive, for we here assume that the rate of covering of the primary rocks by sediments was uniform. It would not be so, however, for the rate of supply of original sediment must have been continually diminishing during geological time, and hence we may assume that the rate of advance of the sediments on the primary rocks has also been diminishing. Now we may probably take, as a fair assumption, that the sediment-covered area was at any instant increasing at a rate proportionate to the rate of supply of sediment; that is, to the area of primary rocks then exposed. On this assumption the age is found to be 87 millions of years.
THE AGE BY THE SODIUM OF THE OCEAN I have next to lay before you a quite different method. I have already touched upon the chemistry of the ocean, and on the remarkable fact that the sodium contained in it has been preserved, practically, in its entirety from the beginning of geological time. That the sea is one of the most beautiful and magnificent sights in Nature, all admit. But, I think, to those who know its story its beauty and magnificence are ten-fold increased. Its saltness it due to no magic mill. It is the dissolved rocks of the Earth which give it at once its brine, its strength, and its buoyancy. The rivers which we say flow with "fresh" water to the sea nevertheless contain those traces of salt which, collected over the long ages, occasion the saltness of the ocean. Each gallon of river water contributes to the final result; and this has been going on since the beginning of our era. The mighty total of the rivers is 6,500 cubic miles of water in the year! There is little doubt that the primeval ocean was in the condition of a fresh-water lake. It can be shown that a primitive and more rapid solution of the original crust of the Earth by the slowly cooling ocean would have given rise to relatively small salinity. The fact is, the quantity of salts in the ocean is enormous. We are only now concerned with the sodium; but if we could extract all the rock-salt (the chloride of sodium) from the ocean we should have enough to cover the entire dry land of the Earth to a depth of 400 feet. It is this gigantic quantity which is going to enter into our estimate of the Earth's age. The calculated mass of sodium contained in this rock-salt is 14,130 million million tonnes. If now we can determine the rate at which the rivers supply sodium to the ocean, we can determine the age.[1] As the result of many thousands of river analyses, the total amount of sodium annually discharged to the ocean NOTE: [1] _Trans. R.D.S._, 1899. A paper by Edmund Halley, the astronomer, in the _Philosophical Transactions of the Royal Society_ for 1715, contains a suggestion for finding the age of the world by the following procedure. He proposes to make observations on the saltness of the seas and ocean at intervals of one or more centuries, and from the increment of saltness arrive at their age. The measurements, as a matter of fact, are impracticable. The salinity would only gain (if all remained in solution) one millionth part in Too years; and, of course, the continuous rejection of salts by the ocean would invalidate the method. The last objection also invalidates the calculation by T. Mellard Reade (_Proc. Liverpool Geol. Soc._, 1876) of a minor limit to the age by the calcium sulphate in the ocean. Both papers were quite unknown to me when working out my method. Halley's paper was, I think, only brought to light in 1908. by all the rivers of the world is found to be probably not far from 175 million tonnes.[1] Dividing this into the mass of oceanic sodium we get the age as 80.7 millions of years. Certain corrections have to be applied to this figure which result in raising it to a little over 90 millions of years. Sollas, as the result of a careful review of the data, gets the age as between 80 and 150 millions of years. My own result[2] was between 80 and 90 millions of years; but I subsequently found that upon certain extreme assumptions a maximum age might be arrived at of 105 millions of years.[3] Clarke regards the 80.7 millions of years as certainly a maximum in the light of certain calculations by Becker.[4] [1] F. W. Clarke, _A Preliminary Study of Chemical Denudation_ (Smithsonian Miscellaneous Collections, 1910). [2] _Loc. cit._ [3] "The Circulation of Salt and Geological Time" (Geol. Mag., 1901, p. 350). [4] Becker (loc. cit.), assuming that the exposed igneous and archaean rocks alone are responsible for the supply of sodium to the ocean, arrives at 74 millions of years as the geological age. This matter was discussed by me formerly (Trans. R.D.S., 1899, pp. 54 _et seq._). The assumption made is, I believe, inadmissible. It is not supported by river analyses, or by the chemical character of residual soils from sedimentary rocks. There may be some convergence in the rate of solvent denudation, but--as I think on the evidence--in our time unimportant. The order of magnitude of these results cannot be shaken unless on the assumption that there is something entirely misleading in the existing rate of solvent denudation. On the strength of the results of another and entirely different method of approaching the question of the Earth's age (which shall be presently referred to), it has been contended that it is too low. It is even asserted that it is from nine to fourteen times too low. We have then to consider whether such an enormous error can enter into the method. The measurements involved cannot be seriously impugned. Corrections for possible errors applied to the quantities entering into this method have been considered by various writers. My own original corrections have been generally confirmed. I think the only point left open for discussion is the principle of uniformitarianism involved in this method and in the methods previously discussed. In order to appreciate the force of the evidence for uniformity in the geological history of the Earth, it is, of course, necessary to possess some acquaintance with geological science. Some of the most eminent geologists, among whom Lyell and Geikie may be mentioned, have upheld the doctrine of uniformity. It must here suffice to dwell upon a few points having special reference to the matter under discussion. The mere extent of the land surface does not, within limits, affect the question of the rate of denudation. This arises from the fact that the rain supply is quite insufficient to denude the whole existing land surface. About 30 per cent. of it does not, in fact, drain to the ocean. If the continents become invaded by a great transgression of the ocean, this "rainless" area diminishes: and the denuded area advances inwards without diminution. If the ocean recedes from the present strand lines, the "rainless" area advances outwards, but, the rain supply being sensibly constant, no change in the river supply of salts is to be expected. Age-long submergence of the entire land, or of any very large proportion of what now exists, is negatived by the continuous sequence of vast areas of sediment in every geologic age from the earliest times. Now sediment-receiving areas always are but a small fraction of those exposed areas whence the sediments are supplied.[1] Hence in the continuous records of the sediments we have assurance of the continuous exposure of the continents above the ocean surface. The doctrine of the permanency of the continents has in its main features been accepted by the most eminent authorities. As to the actual amount of land which was exposed during past times to denudative effects, no data exist to show it was very different from what is now exposed. It has been estimated that the average area of the North American continent over geologic time was about eight-tenths of its existing area. Restorations of other continents, so far as they have been attempted, would not suggest any more serious divergency one way or the other.
In this table the estimated number of tonnes of matter in solution, which for every square mile of area the rivers convey to the ocean in one year, is given in the first column. These results are compiled by Clarke from a very large number of analyses of river waters. The second column of the table gives the mean heights in metres above sea level of the several continents, as cited by Arrhenius. Of all the denudation results given in the table, those relating to North America and to Europe are far the most reliable. Indeed these may be described as highly reliable, being founded on some thousands of analyses, many of which have been systematically pursued through every season of the year. These show that Europe with a mean altitude of less than half that of North America sheds to the ocean 25 per cent. more salts. A result which is to be expected when the more important factors of solvent denudation are given intelligent consideration and we discriminate between conditions favouring solvent and detrital denudation respectively: conditions in many cases antagonistic. Hence if it is true, as has been stated, that we now live in a period of exceptionally high continental elevation, we must infer that the average supply of salts to the ocean by the rivers of the world is less than over the long past, and that, therefore, our estimate of the age of the Earth as already given is excessive. There is, however, one condition which will operate to unduly diminish our estimate of geologic time, and it is a condition which may possibly obtain at the present time. If the land is, on the whole, now sinking relatively to the ocean level, the denudation area tends, as we have seen, to move inwards. It will thus encroach upon regions which have not for long periods drained to the ocean. On such areas there is an accumulation of soluble salts which the deficient rivers have not been able to carry to the ocean. Thus the salt content of certain of the rivers draining to the ocean will be influenced not only by present denudative effects, but also by the stored results of past effects. Certain rivers appear to reveal this unduly increased salt supply those which flow through comparatively arid areas. However, the flowoff of such tributaries is relatively small and the final effects on the great rivers apparently unimportant--a result which might have been anticipated when the extremely slow rate of the land movements is taken into account. The difficulty of effecting any reconciliation of the methods already described and that now to be given increases the interest both of the former and the latter.
THE AGE BY RADIOACTIVE TRANSFORMATIONS Rutherford suggested in 1905 that as helium was continually being evolved at a uniform rate by radioactive substances (in the form of the alpha rays) a determination of the age of minerals containing the radioactive elements might be made by measurements of the amount of the stored helium and of the radioactive elements giving rise to it, The parent radioactive substances are--according to present knowledge--uranium and thorium. An estimate of the amounts of these elements present enables the rate of production of the helium to be calculated. Rutherford shortly afterwards found by this method an age of 240 millions of years for a radioactive mineral of presumably remote age. Strutt, who carried his measurements to a wonderful degree of refinement, found the following ages for mineral substances originating in different geological ages:
Periods of time much less than, and very inconsistent with, these were also found. The lower results are, however, easily explained if we assume that the helium--which is a gas under prevailing conditions--escapes in many cases slowly from the mineral. Another product of radioactive origin is lead. The suggestion that this substance might be made available to determine the age of the Earth also originated with Rutherford. We are at least assured that this element cannot escape by gaseous diffusion from the minerals. Boltwood's results on the amount of lead contained in minerals of various ages, taken in conjunction with the amount of uranium or parent substance present, afforded ages rising to 1,640 millions of years for archaean and 1,200 millions for Algonkian time. Becker, applying the same method, obtained results rising to quite incredible periods: from 1,671 to 11,470 millions of years. Becker maintained that original lead rendered the determinations indefinite. The more recent results of Mr. A. Holmes support the conclusion that "original" lead may be present and may completely falsify results derived from minerals of low radioactivity in which the derived lead would be small in amount. By rejecting such results as appeared to be of this character, he arrives at 370 millions of years as the age of the Devonian. I must now describe a very recent method of estimating the age of the Earth. There are, in certain rock-forming minerals, colour-changes set up by radioactive causes. The minute and curious marks so produced are known as haloes; for they surround, in ringlike forms, minute particles of included substances which contain radioactive elements. It is now well known how these haloes are formed. The particle in the centre of the halo contains uranium or thorium, and, necessarily, along with the parent substance, the various elements derived from it. In the process of transformation giving rise to these several derived substances, atoms of helium--the alpha rays--projected with great velocity into the surrounding mineral, occasion the colour changes referred to. These changes are limited to the distance to which the alpha rays penetrate; hence the halo is a spherical volume surrounding the central substance. The time required to form a halo could be found if on the one hand we could ascertain the number of alpha rays ejected from the nucleus of the halo in, say, one year, and, on the other, if we determined by experiment just how many alpha rays were required to produce the same amount of colour alteration as we perceive to extend around the nucleus. The latter estimate is fairly easily and surely made. But to know the number of rays leaving the central particle in unit time we require to know the quantity of radioactive material in the nucleus. This cannot be directly determined. We can only, from known results obtained with larger specimens of just such a mineral substance as composes the nucleus, guess at the amount of uranium, or it may be thorium, which may be present. This method has been applied to the uranium haloes of the mica of County Carlow. Results for the age of the halo of from 20 to 400 millions of years have been obtained. This mica was probably formed in the granite of Leinster in late Silurian or in Devonian times. The higher results are probably the least in error, upon the data involved; for the assumption made as to the amount of uranium in the nuclei of the haloes was such as to render the higher results the more reliable. This method is, of course, a radioactive method, and similar to the method by helium storage, save that it is free of the risk of error by escape of the helium, the effects of which are, as it were, registered at the moment of its production, so that its subsequent escape is of no moment.
We shall now briefly review the results on the geological age of the Earth. By methods based on the approximate uniformity of denudative effects in the past, a period of the order of 100 millions of years has been obtained as the duration of our geological age; and consistently whether we accept for measurement the sediments or the dissolved sodium. We can give reasons why these measurements might afford too great an age, but we can find absolutely no good reason why they should give one much too low. By measuring radioactive products ages have been found which, while they vary widely among themselves, yet claim to possess accuracy in their superior limits, and exceed those derived from denudation from nine to fourteen times. In this difficulty let us consider the claims of the radioactive method in any of its forms. In order to be trustworthy it must be true; (1) that the rate of transformation now shown by the parent substance has obtained throughout the entire past, and (2) that there were no other radioactive substances, either now or formerly existing, except uranium, which gave rise to lead. As regards methods based on the production of helium, what we have to say will largely apply to it also. If some unknown source of these elements exists we, of course, on our assumption overestimate the age. As regards the first point: In ascribing a constant rate of change to the parent substance--which Becker (loc. cit.) describes as "a simple though tremendous extrapolation"--we reason upon analogy with the constant rate of decay observed in the derived radioactive bodies. If uranium and thorium are really primary elements, however, the analogy relied on may be misleading; at least, it is obviously incomplete. It is incomplete in a particular which may be very important: the mode of origin of these parent bodies--whatever it may have been--is different to that of the secondary elements with which we compare them. A convergence in their rate of transformation is not impossible, or even improbable, so far as we known. As regards the second point: It is assumed that uranium alone of the elements in radioactive minerals is ultimately transformed to lead by radioactive changes. We must consider this assumption. Recent advances in the chemistry of the radioactive elements has brought out evidence that all three lines of radioactive descent known to us--_i.e._ those beginning with uranium, with thorium, and with actinium--alike converge to lead. There are difficulties in the way of believing that all the lead-like atoms so produced ("isotopes" of lead, as Soddy proposes to call them) actually remain as stable lead in the minerals. For one thing there is sometimes, along with very large amounts of thorium, an almost entire absence of lead in thorianites and thorites. And in some urano--thorites the lead may be noticed to follow the uranium in approximate proportionality, notwithstanding the presence of large amounts of thorium.[1] This is in favour of the assumption that all the lead present is derived from the uranium. The actinium is present in negligibly small amounts.
[1] It seems very difficult at present to suggest an end product for thorium, unless we assume that, by loss of electrons, thorium E, or thorium-lead, reverts to a substance chemically identical with thorium itself. Such a change--whether considered from the point of view of the periodic law or of the radioactive theory would involve many interesting consequences. It is, of course, quite possible that the nature of the conditions attending the deposition of the uranium ores, many of which are comparatively recent, are responsible for the difficulties observed. The thorium and uranium ores are, again, specially prone to alteration.
On the other hand, there is evidence arising from the atomic weight of lead which seems to involve some other parent than uranium. Soddy, in the work referred to, points this out. The atomic weight of radium is well known, and uranium in its descent has to change to this element. The loss of mass between radium and uranium-derived lead can be accurately estimated by the number of alpha rays given off. From this we get the atomic weight of uranium-derived lead as closely 206. Now the best determinations of the atomic weight of normal lead assign to this element an atomic weight of closely 207. By a somewhat similar calculation it is deduced that thorium-derived lead would possess the atomic weight of 208. Thus normal lead might be an admixture of uranium- and thorium-derived lead. However, as we have seen, the view that thorium gives rise to stable lead is beset with some difficulties. If we are going upon reliable facts and figures, we must, then, assume: (a) That some other element than uranium, and genetically connected with it (probably as parent substance), gives rise, or formerly gave rise, to lead of heavier atomic weight than normal lead. It may be observed respecting this theory that there is some support for the view that a parent substance both to uranium and thorium has existed or possibly exists. The evidence is found in the proportionality frequently observed between the amounts of thorium and uranium in the primary rocks.[1] Or: (b) We may meet the difficulties in a simpler way, which may be stated as follows: If we assume that all stable lead is derived from uranium, and at the same time recognise that lead is not perfectly homogeneous in atomic weight, we must, of necessity, ascribe to uranium a similar want of homogeneity; heavy atoms of uranium giving rise to heavy atoms of lead and light atoms of uranium generating light atoms of lead. This assumption seems to be involved in the figures upon, which we are going. Still relying on these figures, we find, however, that existing uranium cannot give rise to lead of normal atomic weight. We can only conclude that the heavier atoms of uranium have decayed more rapidly than the lighter ones. In this connection it is of interest to note the complexity of uranium as recently established by Geiger, although in this case it is assumed that the shorter-lived isotope bears the relation of offspring to the longer-lived and largely preponderating constituent. However, there does not seem to be any direct proof of this as yet.
That we have much to learn respecting our assumptions, whether we pursue the geological or the radioactive methods of approaching the age of our era, is, indeed, probable. Whatever the issue it is certain that the reconciling facts will leave us with much more light than we at present possess either as respects the Earth's history or the history of the radioactive elements. With this necessary admission we leave our study of the Birth-Time of the World. It has led us a long way from Lucretius. We do not ask if other Iliads have perished; or if poets before Homer have vainly sung, becoming a prey to all-consuming time. We move in a greater history, the landmarks of which are not the birth and death of kings and poets, but of species, genera, orders. And we set out these organic events not according to the passing generations of man, but over scores or hundreds of millions of years. How much Lucretius has lost, and how much we have gained, is bound up with the question of the intrinsic value of knowledge and great ideas. Let us appraise knowledge as we would the Homeric poems, as something which ennobles life and makes it happier. Well, then, we are, as I think, in possession today of some of those lost Iliads and Odysseys for which Lucretius looked in vain.[1]
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